Interpretation of the Triton Moment

Abstract

In order to account for the measured magnetic moment of the triton it is necessary to assume that the wave function in the ground state is a linear combination of ${}_{}{}^2{}_{}{}^{}S$, ${}_{}{}^2{}_{}{}^{}P$, ${}_{}{}^4{}_{}{}^{}P$, and ${}_{}{}^4{}_{}{}^{}D$ functions. An attempt is made to determine the amplitudes of these functions from the magnetic moment on the assumption that the intrinsic nucleon moments are additive and relativistic effects are negligible. With certain reasonable assumptions concerning the nature of the wave functions, it is found that the relative probabilities for finding the system in the ${}_{}{}^2{}_{}{}^{}P$, ${}_{}{}^4{}_{}{}^{}P$, ${}_{}{}^4{}_{}{}^{}D$ states satisfy the relation shown by the curves in Fig. 1. Wherever the results would otherwise be arbitrary, the wave functions have been chosen in such a way as to minimize the amount of $P$ state, with the exception that only the lowest one-particle configurations have been considered. If the amplitude of the ${}_{}{}^2{}_{}{}^{}S$ state is taken to be as large as possible, the wave function contains no ${}_{}{}^4{}_{}{}^{}D$ state, 8 percent ${}_{}{}^4{}_{}{}^{}P$ state, and 17 percent ${}_{}{}^2{}_{}{}^{}P$ state. A wave function of this form would seem to indicate that there is a spin-orbit coupling other than the tensor interaction acting among nuclear particles. In the other extreme case that the wave function contains a maximum of the ${}_{}{}^4{}_{}{}^{}D$ function, the ${}_{}{}^2{}_{}{}^{}S$ state probability is zero, the ${}_{}{}^4{}_{}{}^{}D$ probability is 22 percent, the ${}_{}{}^4{}_{}{}^{}P$ is 30 percent, and the ${}_{}{}^2{}_{}{}^{}P$ is 48 percent. If the wave function of ${\mathrm{He}}^3$ has the same form as that of ${\mathrm{H}}^3$, the ${\mathrm{He}}^3$ moment would be expected to lie on one of the curves shown in Fig. 2.